一类原点为幂零奇点的三次系统的中心焦点判定与极限环分支  

Criterion of Center—Focus and Limit Cycle Bifurcation for a Class of Special Cubic System in Which Origin is Nilpotent Singular Point

作　　者：赵倩倩[1] 卜珏萍[1] 毕先兵[1] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410083

出　　处：《河北理工大学学报（自然科学版）》2010年第1期55-59,73,共6页Journal of Hebei Polytechnic University:Social Science Edition

摘　　要：研究一类原点为幂零奇点的三次系统的中心焦点判定和极限环分支问题。对一类三次系统给出了计算原点拟Lyapunov常数的递推公式,并在计算机上用Mathematica推导出该系统原点的前6个拟Lyapunov常数,进而分别推导出原点成为中心和最高细焦点的条件,并在此基础上得到了此系统的扰动系统在原点邻域内恰有6个包围原点的极限环的结论。A class of cubic differential system in which origin is nilpotent singular point is studied in this paper. A recursive formula is derived to compute quasi-Lyapunov constant. Using the recursive formula and computer system--Mathematica, the first six quasi-Lyapunov constant of the system are given, from which the conditions for origin to be a center and the highest degree fine focus are derived. Six limit cycles which origin is surrounded in the neighborhood of origin are obtained when the system is perturbed finely.

关 键 词：三次系统 幂零奇点 拟Lyapunov常数 中心焦点 原点 扰动 极限环分支 

分 类 号：O211.4[理学—概率论与数理统计]